The visitors almost made the perfect start in the opening minute as Michael Ingham was forced to collect Alan Bennett's powerful header via a deflection from Lanre Oyebanjo.
The Minstermen responded immediately with Sander Puri firing a tame effort at Ross Worner, before Harry Pell was inches away from giving Neal Ardley's men the lead as his long-range drive flew narrowly wide.
The Dons made their good work count in the 31st minute as Smith scored his third goal of the season. The forward managed to outmuscle George Taft and collect Andy Frampton's long ball before producing a deft lob over Ingham.
York pushed for an equaliser and top scorer Ryan Jarvis went close only to see Dons defender Barry Fuller block his attempt on the line.
And with 17 minutes remaining AFC Wimbledon sealed the points with Smith having the simplest of finishes from substitute Chris Arthur's pass across the face of goal.